Applying Vectors in the Plane — Quiz

Question 10 • Precalculus

A single-engine plane is flying at 30 mph in the direction cap n 60 degrees cap e A wind is blowing from west to east at 15 mph. Which diagram accurately represents the wind triangle for this plane?

Answer

Image with description On a coordinate plane, an air vector goes up and to the right. Ground vector is higher than the ground vector and forms angle 60 degrees with the x-axis. Wind vector connects the terminal points of the vectors.

Image with description On a coordinate plane, a ground vector goes up and to the right. Air vector is higher than the ground vector and forms angle 60 degrees with the y-axis. Wind vector connects the terminal points of the vectors.

Image with description On a coordinate plane, a ground vector goes up and to the right. Air vector is higher than the ground vector and forms angle 60 degrees with the x-axis. Wind vector connects the terminal points of the vectors.

Image with description On a coordinate plane, an air vector goes up and to the right. Ground vector is higher than the ground vector and forms angle 60 degrees with the y-axis. Wind vector connects the terminal points of the vectors.

Explanation

“North 60° east” means the plane’s air-velocity vector is 60° from the north (y) axis, pointing northeast. The eastward wind adds 15 mph to the plane’s eastward component, so the ground-velocity vector points more toward the east and has a smaller angle from the horizontal than the air vector. Thus the air vector is steeper, as shown in choice B.

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